Let us factor .
We will again consider the equivalent problem of finding the roots, the solutions of the equation

Move the constant term to the other side of the equation:

The magic trick of this method
is to exploit the binomial formula:

If we look at the left side of the equation we want to solve, we see that it matches the first two terms of the binomial formula if b=-3. You always take half of the term in front of the x. Let's write down the binomial formula for b=-3:

But the third term of the binomial formula does not show up in our equation; we make it show up by adding 9 to both sides of our equation:

We have "completed the square"!
Now we use the binomial formula to simplify the left side of our equation (also simplifying the right side):

The rest is easy: we take square roots of both sides, but be careful: there are two possible cases:

In both cases .
We are done, once we solve the two equations for x.

are the two roots of our polynomial.
Here is the factorization of our polynomial.